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Bessel phase functions: calculation and application

journal contribution
posted on 2023-05-19, 05:03 authored by Horsley, DE
The Bessel phase functions are used to represent the Bessel functions as a positive modulus and an oscillating trigonometric term. This decomposition can be used to aid root-finding of certain combinations of Bessel functions. In this article, we give some new properties of the modulus and phase functions and some asymptotic expansions derived from differential equation theory. We find a bound on the error of the first term of this asymptotic expansion and give a simple numerical method for refining this approximation via standard routines for the Bessel functions. We then show an application of the phase functions to the root finding problem for linear and cross-product combinations of Bessel functions. This method improves upon previous methods and allows the roots in ascending order of these functions to be calculated independently. We give some proofs of correctness and global convergence.

History

Publication title

Numerische Mathematik

Volume

136

Pagination

679-702

ISSN

0029-599X

Department/School

School of Natural Sciences

Publisher

Springer-Verlag

Place of publication

175 Fifth Ave, New York, USA, Ny, 10010

Rights statement

Copyright 2016 Springer-Verlag Berlin Heidelberg

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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